This invention relates to the investigation of earth formations with electromagnetic energy and, more particularly to a method and apparatus for determinig the dielectric properties of subsurface formations by passing electromagnetic energy therethrough. The subject matter of this application is related to subject matter in a copending U.S. Application Ser. No. 390,988 of Levy et al entitled METHOD AND APPARATUS FOR INVESTIGATING EARTH FORMATIONS, filed of even date herewith and assigned to the same assignee as the present invention.
There have been previously proposed various techniques for measuring the dielectric constant or electric permittivity of subsurface formations. Prior investigators have recognized that the dielectric constant of the different materials of earth formations vary widely (e.g. 2.2 for oil, 7.5 for limestone and 80 for water) and that the measurement of dielectric properties therefore holds promise of being a useful means of formation evaluation. As an illustration, if the lithology and degree of water saturation of a particular formation are determined from conventional well logging techniques, it is recognized that porosity should be determinable if the dielectfic constant of the material could be obtained. Similarly, if the lithology and porosity were given as "knowns," information as to the degree of water saturation should be obtainable by measuring the dielectric constant of the formation.
Previously proposed instruments for the logging of dielectric constants in a borehole have not achieved hoped-for success for a variety of reasons. To understand the difficulties which have been encountered by investigators it is helpful to examine momentarily the general nature of the dielectric constant of a lossy material which can be expressed as a complex quantity of the form EQU .epsilon.* = .epsilon.' + j .epsilon."
The real part .epsilon.' in this equation represents the "true" dielectric constant of the material in lossless form; i.e., the measure of displacement currents for a particular electric field in the material if it were lossless. The imaginary part .epsilon." represents the "loss factor" of the material; i.e., the losses due to conduction and relaxation effects. Most previous efforts have been concerned with determining the value of .epsilon.' for a particular portion of subsurface formation. However, subsurface formation materials have appreciable conductivity and thus a significant loss factor .epsilon." which is often greater in magnitude than .epsilon.'. Since loss factor is necessarily measured to some extent when attempting to measure .epsilon.', the attainment of accurate values of .epsilon.' has been largely frustrated by the presence of a significant loss factor.
The U.S. Pat. No. 3,551,797 of Gouilloud et al. teaches a technique wherein high frequency electromagnetic energy is emitted into a formation. The resultant propagated electromagnetic waves are measured to determine properties of the formation through which the waves have passed. The patent disclosure is largely concerned with determining formation conductivity which is achieved by indirectly measuring the "skin depth" of the traversed formation. It is instructive as background herein to examine the theory underlying the skin depth measurement of that patent which is described briefly as follows: The magnetic field strength H.sub.z at a distance z, for large values of z, from a transmitter, is expressed in Gouilloud et al as ##EQU1## where e is the natural logarithm base, H.sub.o is the magnetic field strength at the transmitter, and .delta. the skin depth defined as ##EQU2## where .omega. is the radian frequency of the transmitter signal, .mu. is the magnetic permeability of the formation, generally considered a constant, and .sigma. is the conductivity of the formation. (A similar equation could be set forth to express the electric field.) Equation (1) indicates that the electromagnetic field is attenuated and phase shifted as the distance term z increases; i.e., as the electromagnetic energy propagates through the formations. The degree of phase shift is expressed by the term -j(z/.delta.) and the degree of attenuation expressed by the term -(z/.delta.). The composite term (1/.delta.)(1+j) is defined as the propagation constant, the term 1/.delta. being the attenuation constant and the term j(1/.delta.) being the phase constant.
In the Gouilloud et al patent, the attenuation constant and the phase constant are indicated as having the same magnitude and, consequently, skin depth can be determined from either attenuation measurements or phase measurements. The attenuation calculation involves the measurement of the amplitude of the electromagnetic energy at receiving locations spaced a distance .DELTA.l apart in the formation. The amplitudes at the two receiving locations, designated A.sub.1 and A.sub.2, are used to calculate the skin depth .delta. in accordance with the relationship ##EQU3## Alternately, the phase difference between the two receiving locations, designated as .DELTA..phi., is used to calculate skin depth in accordance with the relationship ##EQU4## Knowing .delta., the conductivity of the formation, .sigma., is determined from equation (2).
The described technique of Gouilloud et al is predicated on the substantial equality of the attenuation and phase constants of the electromagnetic energy. This assumption holds whenever ##EQU5## where .epsilon. is the dielectric constant of the material through which the wave is propagating. The term .sigma./.omega..epsilon., known as the "loss tangent", is the ratio of a quantity that relates to lossy conduction currents (.sigma.) with respect to a quantity that relates to displacement currents (.omega..epsilon.). (Note that the loss tangent, a measure of relative conduction losses, contributes to the loss factor term .epsilon." introduced above.) Thus, if .sigma. is substantial, and the operating frequency relatively low, the propagation constant of the electromagnetic wave has little dependence upon the material's true dielectric constant. This is evidenced by equation (2) (which does not depend upon dielectric constant) and the subsequent Gouilloud et al expression for propagation constant, (1/.delta.) (1+j).
As was initially stated, past attempts at determining true dielectric constant have met little success. It is an object of the present invention to utilize a propagating electromagnetic wave type of technique to determine the true dielectric constant of a subsurface formation under investigation.